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• Cauchy-Schwarz Inequality
  ...verrightarrow{w}</math> and <math>\| \overrightarrow{v} \|</math> is the [[norm]] of <math>\overrightarrow{v}</math>, <cmath>\|\overrightarrow{v}\| \|\over
  13 KB (2,048 words) - 15:28, 22 February 2024
• Partition of an interval
  ===Norm=== The '''norm''' of a partition <math>\mathcal{P}</math> is defined as <math>\|\mathcal{P
  1 KB (178 words) - 20:34, 6 March 2022
• Gauge
  ...ge''' is a more accurate way to 'measure' a partition that its [[Partition|norm]].
  788 bytes (140 words) - 08:53, 16 February 2008
• Henstock-Kurzweil integral
  ...'measure' a partition more accurately than its [[Partition of an interval|norm]]
  2 KB (401 words) - 09:46, 31 January 2018
• Chain Rule
  ...That's good. (<math>\Vert f'(g(x_o)) \Vert_2</math> is the <math>2</math>-norm of the matrix <math>f'(g(x_0))</math>.) ...orm of the input of <math>E_f</math>, we will also have to multiply by the norm of the input of <math>E_f</math>.
  12 KB (2,377 words) - 11:48, 22 July 2009
• Absolute value
  * [[Norm]]
  2 KB (368 words) - 10:37, 5 January 2009
• Finite Fourier Analysis
  ...vectors {<math>{f_n : n=0,\ldots, N-1}</math>} is orthogonal, and that the norm of <math>f_n</math> is <math>\sqrt{N}</math>. We can normalize <math>f_n</
  4 KB (724 words) - 19:15, 9 September 2006
• Euclidean domain
  ...a function <math>N:R\setminus\{0\}\to \mathbb Z_{\ge0}</math> called a '''Norm''' such that for all nonzero <math>a,b\in R</math> there are <math>q,r\in R * The ring of [[integers]] <math>\mathbb Z</math> with norm given by <math>N(a) = |a|</math>.
  2 KB (357 words) - 15:28, 22 August 2009
• Fermat's Two Squares Theorem
  then <math>(a+bi)</math> and <math>(a-bi)</math> both have a prime norm; hence they are both Gaussian primes. Hence any such representation is uni
  4 KB (612 words) - 12:10, 30 May 2019
• Euler's Four-Square Identity
  ...<math>Y: = y_1 + y_2 i + y_3 j + y_4 k</math>. Recall that the quaternion norm of a number <math>a + bi + cj + dk</math>, written as <math>|a + bi + cj + ...entity simply reads <math>|XY|^2 = |X|^2 |Y|^2</math>; i.e. the quaternion norm is multiplicative.
  1 KB (179 words) - 23:24, 5 November 2019
• 2013 AIME II Problems/Problem 12
  ...t need <math>2a</math> to be integral, because <math>a^2+b^2</math> IS the norm of the root! (Note that it is not necessary to multiply by the real root. T ...-19, ...., 0, 0.5, ..., 19.5</math> or <math>79</math> solutions. When the norm is <math>13</math>, the <math>a</math> term has <math>51</math> possibiliti
  8 KB (1,393 words) - 19:00, 24 May 2023
• Algebraic number theory
  ...\sqrt{-n})(x-y\sqrt{-n})</math> is the product of two elements - and the [[norm]] of one. The case of <math>n=1</math>, in particular, leads to [[factoriza ==The norm map==
  10 KB (1,646 words) - 15:04, 28 May 2020
• 1973 IMO Problems/Problem 1
  ...c\pi 2</math> with the vector of norm <math>\ge 1</math>, so their sum has norm <math>\ge 1</math>, and we're done.
  1 KB (227 words) - 15:45, 29 January 2021
• 2022 AIME I Problems/Problem 14
  ...it suffices to find an element of <math>\mathbb Z[\omega]</math> with the norm <math>73^2</math>.
  16 KB (2,730 words) - 02:56, 4 January 2023
• Crusade
  ...rer of any spectacular hardship. For five hundred years, this has been the norm. Genocide and slaughter are but light condiments of a meal.[/i]
  36 KB (5,892 words) - 20:26, 11 September 2022
• Orthonormal
  ...eir [[dot product]] is zero. The "normal" part refers to the fact that the norm (magnitude) <math>||v_k||</math> of every vector in the set is one, since <
  3 KB (518 words) - 22:17, 26 June 2023